Positivity Sized-Up Effectively

Abstract

Causal inference relies on several key identifying assumptions, including positivity: all treatment levels must have non-zero probability for every possible covariate combination. Violations lead to unreliable causal effect estimates, yet positivity is often overlooked, and existing diagnostics have limitations. This assumption is particularly relevant for observational data, because treatment assignment is not independent of confounders. To remove this dependence, Inverse probability of treatment weighting (IPTW) estimators can be used. However, IPTW relies on the positivity assumption, and near-violations lead to extreme weights and unstable estimates. We investigate effective sample size (ESS) as a practical diagnostic for evaluating the estimability of causal effects in the face of near-positivity violations. The key contribution is a theoretical definition of ‘targeted ESS’ that aligns with causal inference. Targeted ESS can quantify how many observations effectively contribute to weighted estimates and can serve as an intuitive tool for communicating positivity concerns. Through analysis and simulations, we demonstrate its strengths and limitations. Notably, targeted ESS cannot detect severe cases of positivity violations or propensity model misspecifications. Additionally, we show why conventional ESS is not generally suitable in this setting. This work offers practical guidance for assessing IPTW estimate reliability in observational causal inference.